Question: Simplify the following expression: $ x = \dfrac{-1}{5} + \dfrac{-10k}{-8k + 9} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-8k + 9}{-8k + 9}$ $ \dfrac{-1}{5} \times \dfrac{-8k + 9}{-8k + 9} = \dfrac{8k - 9}{-40k + 45} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-10k}{-8k + 9} \times \dfrac{5}{5} = \dfrac{-50k}{-40k + 45} $ Therefore $ x = \dfrac{8k - 9}{-40k + 45} + \dfrac{-50k}{-40k + 45} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{8k - 9 - 50k}{-40k + 45} $ $x = \dfrac{-42k - 9}{-40k + 45}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{42k + 9}{40k - 45}$